ECE230AHomework3

ECE230AHomework3 - “ β ”(a Find the dispersion...

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ECE230A Homework #3 Homework due: November 18, 2010 1. The intrinsic carrier concentration at room temperature (300K) for Ge and Si is 2.3x10 13 cm -3 and 1.1x10 10 cm -3 , respectively. The bandgap energy Eg, Ge =0.67 eV, Eg, Si = 1.1 eV. (a) Find the intrinsic concentrations of Ge and Si at 400K. (b) If Si is doped with shallow acceptors and shallow donors: N A =2x10 15 cm -3 and N D =1x10 15 cm -3 . Calculate the Fermi energy above the valence band edge. (c) If N d > N a , derive ] exp[ ) ( 2 kT E E N n N N n N n d c c a d a = + where E d is the energy of the donor state. 2. Aluminum has a simple cubic structure with an atomic mass “M” and spring constant
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Unformatted text preview: “ β ”, (a) Find the dispersion relation ω (k) for phonons in the 1st BZ a k k k a z y x π ≤ ≤ − , , . (b) Using the relation β /M=Y/ ρ a 2 (Y: Young’s modulus = 1.14x10 11 Nt/m 2 , a=4.03Å, and ρ =2.73 g/cm 3 ), calculate the maximum phonon energy in electron volt (eV). (c) Calculate the speed of the sound in aluminum. 3. Assuming an E-k relation: ߝ ൌ ߝ ௖ ൅ ԰ మ ௠௔ మ ൤1 െ ܿ݋ݏ ቂቀ݇ െ గ ସ௔ ቁ ܽቃ൨ . Plot the band diagram, the group velocity, and the effective mass over the first Brillouin Zone....
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